Can there be more than one tangent at one point on a circle? Why?

Answer 1

Not to a circle in two dimensions as the tangent has to be perpendicular to the radius and so is unique. This is because they all lie in the same plane

BUT in 3-D there is an infinite number of tangents that all lie in the plane at the point of contact with the radius at the point of contact as a normal

The tangent in 2-D is the trace of that plane in 3-D where it cuts the plane containing the circle.

Answer 2

No, the tangent not only goes thru a point on the circle but has a particular slope at that point, since it is perpendicular to the radius at the point of tangency. Two lines thru the same point with the same slope are the same line.

Answer 3

no it is not possible.
the reason lies in the definition of a tanegnt.
a tangent is a line which cuts the circle at a single point.
if two lines are made such that they pass through the same point on the circumferance then they will cut the circle at another point also thus it will not be a tangent.

Answer 4

No. The tangent at any point has the slope at that point. Since each point is unique & the slope at each point is unique, there will be 1 & only 1 tangent line.

Answer 5

Since a circle on plane geometry is nonsingular (smooth), at a given point on the circle, it is impossible to have more than one tangent line.

Answer 6

suppose A belongs to a circle with center O, let AB be tangent to the circle, that means that AB is normal to radius OA; now assume that a line AC is also a tangent, then AC is also normal to OA; now according to a notorious theorem of Euclid’s geometry (I don’t remember exactly the theorem’s name) only one perpendicular to the line OA can be traced through point A!

Answer 7

i guess not. considering the law of vectors each point can have only one direction at any given point of time. as if a point has a tangent, at that given time interval it has to have only that one tangent as the direction cannot be changed, for, a particale simultaneously cannot have two directions.

Answer 8

no. there can be only two tangents at one point on a circle...

Answer 9

no because...wait... i think i got this question wrong on the psat....crap....i just remember the proctor during corrections said no....i forgot why.....